Subgroups — #36523894

Order 22784.

730 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029333	C₂	1	1	yes	maximal, characteristic, complemented
2	#26029276	C₂	1	1	yes	maximal, characteristic
3	SD₁₆⋊#10623494	C₂	1	4	yes	maximal, complemented
4	SD₁₆×#10623494	C₂	1	4	yes	maximal, complemented
5	#26019000	C₂	1	1	yes	maximal, characteristic, complemented
6	#26018647	C₂	1	1	yes	maximal, characteristic, complemented
7	#26018643	C₂	1	1	yes	maximal, characteristic
8	#26018535	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×SD₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic
10	Q₈×#10623494	—	2	2	no	—
11	Q₈×#10623494	C₂²	1	4	yes	complemented
12	D₄×#10623494	—	2	2	no	—
13	D₄×#10623494	C₂²	1	4	yes	—
14	#19151651	—	2	2	no	—
15	#19151651	C₂²	1	1	yes	characteristic
16	#19151651	C₂²	1	1	yes	characteristic
17	#19151651	C₂²	1	1	yes	characteristic
18	#19151651	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊#10623494	—	2	2	no	—
20	#19151351	C₂²	1	2	yes	complemented
21	#19151349	C₂²	1	2	yes	complemented
22	Q₈⋊#10623494	C₂²	1	4	yes	complemented
23	D₄⋊#10623494	C₂²	1	4	yes	—
24	#19151319	C₂²	1	2	yes	complemented
25	C₈×#10623494	C₂²	1	2	yes	complemented
26	C₂²×SD₁₆×C₈₉	C₄	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
29	C₄×SD₁₆×C₈₉	C₄	1	2	yes	—
30	C₄×SD₁₆×C₈₉	C₄	1	2	yes	—
31	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
32	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
33	C₂×#106×C₈₉	C₄	1	1	yes	characteristic
34	C₂×#103×C₈₉	C₄	1	1	yes	characteristic
35	C₂×#102×C₈₉	C₄	1	1	yes	characteristic
36	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
37	C₂²×#10623494	—	2	4	no	—
38	C₄⋊#10623494	—	2	4	no	—
39	C₄⋊#10623494	—	2	1	no	—
40	C₄⋊#10623494	D₄	1	2	yes	—
41	C₄⋊#10623494	C₂³	1	2	yes	—
42	C₄⋊#10623494	C₂³	1	2	yes	—
43	C₂²⋊#10623494	—	2	4	no	—
44	C₂²⋊#10623494	—	2	1	no	—
45	C₂²⋊#10623494	—	2	1	no	—
46	C₂²⋊#10623494	—	2	1	no	—
47	C₂²⋊#10623494	D₄	1	2	yes	—
48	C₄×#10623494	—	2	4	no	—
49	C₄×#10623494	—	2	1	no	—
50	C₄×#10623494	—	2	1	no	—
51	C₄×#10623494	C₂³	1	2	yes	—
52	C₄×#10623494	C₂³	1	2	yes	—
53	C₂²×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
54	C₂²×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
55	C₂³×C₄×C₈₉	—	2	1	no	—
56	C₂×SD₁₆×C₈₉	C₈	1	8	yes	complemented
57	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	—
58	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	—
59	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
61	C₄×Q₈×C₈₉	—	2	1	no	—
62	C₄×Q₈×C₈₉	—	2	1	no	—
63	C₄×Q₈×C₈₉	C₂×C₄	1	2	yes	—
64	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
65	C₄×D₄×C₈₉	—	2	1	no	—
66	C₄×D₄×C₈₉	—	2	1	no	—
67	C₄×D₄×C₈₉	C₂×C₄	1	2	yes	—
68	C₄×D₄×C₈₉	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
73	C₂×C₄²×C₈₉	—	2	1	no	—
74	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
75	#106×C₈₉	C₂×C₄	1	2	yes	—
76	#106×C₈₉	C₂×C₄	1	2	yes	—
77	#103×C₈₉	C₂×C₄	1	2	yes	—
78	#103×C₈₉	C₂×C₄	1	2	yes	—
79	#102×C₈₉	C₂×C₄	1	2	yes	—
80	#102×C₈₉	C₂×C₄	1	2	yes	—
81	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
82	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
83	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
84	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
85	C₂×#10623494	—	2	2	no	—
86	C₂×#10623494	—	2	2	no	—
87	C₂×#10623494	—	2	2	no	—
88	C₂×#10623494	—	8	4	no	—
89	C₂×#10623494	C₂×D₄	1	4	yes	—
90	C₂⁴×C₈₉	—	2	1	no	—
91	C₂×Q₈×C₈₉	—	2	1	no	—
92	C₂×Q₈×C₈₉	—	2	2	no	—
93	C₂×Q₈×C₈₉	C₂×C₈	1	4	yes	complemented
94	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
95	C₂×D₄×C₈₉	—	2	1	no	—
96	C₂×D₄×C₈₉	—	2	2	no	—
97	C₂×D₄×C₈₉	C₂×C₈	1	4	yes	—
98	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₈₉	—	2	1	no	—
100	C₂²×C₄×C₈₉	—	2	1	no	—
101	C₂²×C₄×C₈₉	—	2	1	no	—
102	C₂²×C₄×C₈₉	—	2	2	no	—
103	C₂²×C₄×C₈₉	—	2	2	no	—
104	C₂²×C₄×C₈₉	—	8	2	no	—
105	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
108	SD₁₆×C₈₉	C₂×C₈	1	8	yes	complemented
109	SD₁₆×C₈₉	C₂×C₈	1	8	yes	complemented
110	C₂×C₈×C₈₉	—	2	2	no	—
111	C₂×C₈×C₈₉	C₂×C₈	1	4	yes	complemented
112	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
116	C₄⋊C₄×C₈₉	—	2	2	no	—
117	C₄⋊C₄×C₈₉	—	2	1	no	—
118	C₄⋊C₄×C₈₉	—	2	1	no	—
119	C₄⋊C₄×C₈₉	—	2	2	no	—
120	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
121	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
122	C₂²⋊C₄×C₈₉	—	2	2	no	—
123	C₂²⋊C₄×C₈₉	—	2	2	no	—
124	C₄²×C₈₉	—	2	2	no	—
125	C₄²×C₈₉	—	2	2	no	—
126	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
127	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₈₉	#41	1	1	yes	characteristic
129	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
130	C₂³×C₈₉	—	2	2	no	—
131	C₂³×C₈₉	—	2	4	no	—
132	C₂³×C₈₉	—	8	1	no	—
133	C₂³×C₈₉	—	8	1	no	—
134	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
135	Q₈×C₈₉	—	2	2	no	—
136	Q₈×C₈₉	—	2	4	no	—
137	Q₈×C₈₉	C₂²×C₈	1	4	yes	—
138	D₄×C₈₉	—	2	2	no	—
139	D₄×C₈₉	—	2	4	no	—
140	D₄×C₈₉	C₂²×C₈	1	4	yes	—
141	C₂×C₄×C₈₉	—	2	2	no	—
142	C₂×C₄×C₈₉	—	2	4	no	—
143	C₂×C₄×C₈₉	—	2	2	no	—
144	C₂×C₄×C₈₉	—	2	2	no	—
145	C₂×C₄×C₈₉	—	2	2	no	—
146	C₂×C₄×C₈₉	—	4	1	no	—
147	C₂×C₄×C₈₉	—	4	4	no	—
148	C₂×C₄×C₈₉	—	8	2	no	—
149	C₂×C₄×C₈₉	—	8	1	no	—
150	C₂×C₄×C₈₉	—	8	1	no	—
151	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₈₉	C₂²×C₈	1	2	yes	—
155	C₂×C₄×C₈₉	#131	1	2	yes	—
156	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
159	C₈×C₈₉	—	2	1	no	—
160	C₈×C₈₉	—	2	1	no	—
161	C₈×C₈₉	C₂²×C₈	1	2	yes	—
162	C₈×C₈₉	C₂²×C₈	1	2	yes	—
163	#10623494	—	2	4	no	—
164	#10623494	—	4	2	no	—
165	#10623494	—	4	2	no	—
166	#10623494	—	4	2	no	—
167	C₂²×C₈₉	—	2	1	no	—
168	C₂²×C₈₉	—	2	1	no	—
169	C₂²×C₈₉	—	2	4	no	—
170	C₂²×C₈₉	—	4	2	no	—
171	C₂²×C₈₉	—	4	2	no	—
172	C₂²×C₈₉	—	8	4	no	—
173	C₂²×C₈₉	C₈×D₄	1	2	yes	—
174	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
175	C₄×C₈₉	—	2	4	no	—
176	C₄×C₈₉	—	2	1	no	—
177	C₄×C₈₉	—	2	1	no	—
178	C₄×C₈₉	—	2	1	no	—
179	C₄×C₈₉	—	4	2	no	—
180	C₄×C₈₉	—	4	2	no	—
181	C₄×C₈₉	C₈×D₄	1	2	yes	—
182	C₄×C₈₉	C₂³×C₈	1	1	yes	characteristic
183	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
184	C₄×C₈₉	#577	1	2	yes	—
185	#17855	—	89	1	no	maximal, Sylow
186	C₂×C₈₉	—	2	2	no	—
187	C₂×C₈₉	—	4	4	no	—
188	C₂×C₈₉	C₂×C₈×D₄	1	1	yes	characteristic
189	C₂×C₈₉	#2949	1	1	yes	characteristic
190	C₂×C₈₉	#2957	1	1	yes	characteristic
191	#2982	—	89	1	no	—
192	#2972	—	89	1	no	—
193	C₂×C₄×SD₁₆	D₈₉	1	1	yes	characteristic
194	SD₁₆⋊C₈	—	89	4	no	—
195	C₈×SD₁₆	—	89	4	no	—
196	#1564	—	89	1	no	—
197	#1479	—	89	1	no	—
198	#1478	—	89	1	no	—
199	#1450	—	89	1	no	—
200	C₈₉	#17855	1	1	yes	characteristic, complemented, Sylow
201	C₂²×SD₁₆	Dic₈₉	1	1	yes	characteristic
202	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
203	C₂×C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
204	C₈×Q₈	—	89	4	no	—
205	C₈×Q₈	—	178	2	no	—
206	C₄×SD₁₆	Dic₈₉	1	2	yes	—
207	C₄×SD₁₆	Dic₈₉	1	2	yes	—
208	C₄×SD₁₆	C₂×D₈₉	1	2	yes	—
209	C₄×SD₁₆	C₂×D₈₉	1	2	yes	—
210	C₈×D₄	—	89	4	no	—
211	C₈×D₄	—	178	2	no	—
212	#431	—	89	1	no	—
213	#431	—	89	1	no	—
214	#431	—	89	1	no	—
215	#431	—	89	1	no	—
216	#431	—	178	2	no	—
217	C₂×#106	Dic₈₉	1	1	yes	characteristic
218	C₂×#103	Dic₈₉	1	1	yes	characteristic
219	C₂×#102	Dic₈₉	1	1	yes	characteristic
220	C₂×C₂²⋊C₈	—	178	2	no	—
221	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
222	#335	—	89	2	no	—
223	#334	—	89	2	no	—
224	Q₈⋊C₈	—	89	4	no	—
225	D₄⋊C₈	—	89	4	no	—
226	#322	—	89	2	no	—
227	C₈²	—	89	2	no	—
228	C₂²×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
229	C₂²×D₄	C₂×Dic₈₉	1	1	yes	characteristic
230	C₂³×C₄	—	2	1	no	—
231	C₂×SD₁₆	#10623494	1	8	yes	complemented
232	C₂×SD₁₆	C₂×Dic₈₉	1	2	yes	—
233	C₂×SD₁₆	C₂×Dic₈₉	1	2	yes	—
234	C₂²×C₈	—	178	4	no	—
235	C₂²×C₈	C₂×Dic₈₉	1	1	yes	characteristic
236	C₂²×C₈	C₂×Dic₈₉	1	1	yes	characteristic
237	C₄×Q₈	—	2	1	no	—
238	C₄×Q₈	—	2	1	no	—
239	C₄×Q₈	C₂×Dic₈₉	1	2	yes	—
240	C₄×Q₈	C₂²×D₈₉	1	2	yes	—
241	C₄×D₄	—	2	1	no	—
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	C₂×Dic₈₉	1	2	yes	—
244	C₄×D₄	C₂²×D₈₉	1	2	yes	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
247	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
248	C₂×C₂²⋊C₄	—	2	1	no	—
249	C₂×C₄²	—	2	1	no	—
250	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
251	#106	C₂×Dic₈₉	1	2	yes	—
252	#106	C₂×Dic₈₉	1	2	yes	—
253	C₄⋊C₈	—	89	2	no	—
254	C₄⋊C₈	—	89	2	no	—
255	C₄⋊C₈	—	89	2	no	—
256	C₄⋊C₈	—	178	4	no	—
257	C₄⋊C₈	—	178	1	no	—
258	#103	C₂×Dic₈₉	1	2	yes	—
259	#103	C₂×Dic₈₉	1	2	yes	—
260	#102	C₂×Dic₈₉	1	2	yes	—
261	#102	C₂×Dic₈₉	1	2	yes	—
262	C₂²⋊C₈	—	89	2	no	—
263	C₂²⋊C₈	—	178	4	no	—
264	C₂²⋊C₈	—	178	1	no	—
265	C₂²⋊C₈	—	178	1	no	—
266	C₂²⋊C₈	—	178	1	no	—
267	C₄×C₈	—	89	2	no	—
268	C₄×C₈	—	89	2	no	—
269	C₄×C₈	—	178	4	no	—
270	C₄×C₈	—	178	1	no	—
271	C₄×C₈	—	178	1	no	—
272	C₄×C₈	C₂×Dic₈₉	1	1	yes	characteristic
273	C₄×C₈	C₂×Dic₈₉	1	1	yes	characteristic
274	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
275	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
276	C₂⁴	—	2	1	no	—
277	C₂×Q₈	—	2	1	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	C₂×#10623494	1	4	yes	complemented
280	C₂×Q₈	C₂²×Dic₈₉	1	2	yes	—
281	C₂×D₄	—	2	1	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	C₂×#10623494	1	4	yes	—
284	C₂×D₄	C₂²×Dic₈₉	1	2	yes	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	8	2	no	—
291	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
292	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
293	C₂²×C₄	#13083573	1	1	yes	characteristic
294	SD₁₆	C₂×#10623494	1	8	yes	complemented
295	SD₁₆	C₂×#10623494	1	8	yes	complemented
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	89	4	no	—
298	C₂×C₈	—	178	2	no	—
299	C₂×C₈	—	178	2	no	—
300	C₂×C₈	—	178	2	no	—
301	C₂×C₈	—	712	4	no	—
302	C₂×C₈	C₂×#10623494	1	4	yes	complemented
303	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
304	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
305	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
306	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	C₂²×Dic₈₉	1	2	yes	—
312	C₄⋊C₄	C₂²×Dic₈₉	1	2	yes	—
313	C₂²⋊C₄	—	2	2	no	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	2	no	—
317	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
318	C₄²	D₄×D₈₉	1	1	yes	characteristic
319	C₄²	#13083573	1	1	yes	characteristic
320	C₄²	C₂³×D₈₉	1	1	yes	characteristic
321	C₂³	—	2	2	no	—
322	C₂³	—	2	4	no	—
323	C₂³	—	8	1	no	—
324	C₂³	—	8	1	no	—
325	C₂³	D₄×Dic₈₉	1	1	yes	characteristic
326	Q₈	—	2	4	no	—
327	Q₈	—	2	2	no	—
328	Q₈	C₂²×#10623494	1	4	yes	—
329	D₄	—	2	4	no	—
330	D₄	—	2	2	no	—
331	D₄	C₂²×#10623494	1	4	yes	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	8	2	no	—
340	C₂×C₄	—	8	1	no	—
341	C₂×C₄	—	8	1	no	—
342	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
343	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
344	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
345	C₂×C₄	C₂²×#10623494	1	2	yes	—
346	C₂×C₄	#15668019	1	2	yes	—
347	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
348	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
349	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
350	C₈	—	2	1	no	—
351	C₈	—	2	1	no	—
352	C₈	—	356	2	no	—
353	C₈	—	356	2	no	—
354	C₈	—	356	2	no	—
355	C₈	—	178	4	no	—
356	C₈	C₂²×#10623494	1	2	yes	—
357	C₈	C₂²×#10623494	1	2	yes	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	4	no	—
361	C₂²	—	4	2	no	—
362	C₂²	—	4	2	no	—
363	C₂²	—	8	4	no	—
364	C₂²	D₄×#10623494	1	2	yes	—
365	C₂²	C₂×D₄×Dic₈₉	1	1	yes	characteristic
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	2	4	no	—
370	C₄	—	4	2	no	—
371	C₄	—	4	2	no	—
372	C₄	D₄×#10623494	1	2	yes	—
373	C₄	C₂³×#10623494	1	1	yes	characteristic
374	C₄	C₂×#15668019	1	1	yes	characteristic
375	C₄	#19152404	1	2	yes	—
376	C₂	—	2	2	no	—
377	C₂	—	4	4	no	—
378	C₂	C₂×D₄×#10623494	1	1	yes	characteristic
379	C₂	#26029112	1	1	yes	characteristic
380	C₂	#26029169	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₄×C₈₉	C₂³×C₈
Frattini	C₄²	C₂³×D₈₉
Fitting	C₂×C₄×SD₁₆×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂²×D₄×C₈₉	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₂×C₄×SD₁₆	D₈₉
hypocenter	C₈₉	#17855
LCS	G ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×SD₁₆

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #26029333	C₂	semidirect
3. SD₁₆⋊#10623494	C₂	semidirect
4. SD₁₆×#10623494	C₂	semidirect
5. #26019000	C₂	semidirect
6. #26018647	C₂	semidirect
8. #26018535	C₂	semidirect
11. Q₈×#10623494	C₂²	semidirect
20. #19151351	C₂²	semidirect
21. #19151349	C₂²	semidirect
22. Q₈⋊#10623494	C₂²	semidirect
24. #19151319	C₂²	semidirect
25. C₈×#10623494	C₂²	semidirect
56. C₂×SD₁₆×C₈₉	C₈	semidirect
93. C₂×Q₈×C₈₉	C₂×C₈	semidirect
108. SD₁₆×C₈₉	C₂×C₈	semidirect
109. SD₁₆×C₈₉	C₂×C₈	semidirect
111. C₂×C₈×C₈₉	C₂×C₈	semidirect
200. C₈₉	#17855	semidirect
231. C₂×SD₁₆	#10623494	semidirect
279. C₂×Q₈	C₂×#10623494	semidirect
294. SD₁₆	C₂×#10623494	semidirect
295. SD₁₆	C₂×#10623494	semidirect
302. C₂×C₈	C₂×#10623494	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#26029333	2
#26029276	2
SD₁₆⋊#10623494	2
SD₁₆×#10623494	2
#26019000	2
#26018647	2
#26018643	2
#26018535	2
C₂×C₄×SD₁₆×C₈₉	2
#17855	89